Why does my shifter shake when accelerating?

Such an idiot lol x

NORMAL!!!!!!!!!!!!!!!!! The RPM's are generating torch as well, so the hole drive trains shakes some!

You can take it back the dealership and have one of their mechanics check it out, but I've had a few manual vehicles where the gear shift moved/shook a little bit with acceleration/deceleration and it never seemed to be a problem.

That's nothing to worry about.

4 to 5 thousand RPMs is in the normal range for acceleration. Take it back to the dealership, they'll find the problem.

If it REALLY is a "brand new" car, then take it back to the dealer's service department and ask them to check it.

You're driving a mass produced "whoopty", like the rest of us. The engine is balanced, but not for consistent high RPM's like 8,000+, and you're tranny is balanced but not for consistent high RPM's. So, the faster the crankshaft turns, the faster the tranny flex plate, torque converter, or flywheel turns, the more vibration you will have on a mass produced car. 

Most race cars run between 8,000 to 16,000 RPM's and are balanced to handle those higher RPM's. 

Jet engines run 150K to 250K RPM's and are balanced to just one gram tolerance. 

Misfiring engine, broken motor count, or broken transmission mount.

Tires out of balance or the motor is misfiring.

Year, make and model would be nice.